Sporting host Genk in Group G knowing they must win to have any hope of advancing further in the competition.
Former Belgium coach Vercauteren steered Genk to the Belgian title in 2010/11 before being appointed coach of Al Jazira Club in the United Arab Emirates earlier this year.
When Ricardo Sa Pinto was sacked by Sporting last month, Vercauteren stepped in having been axed by Al Jazira Club himself.
"This is a special match for me, though not in an emotional way," Vercauteren said.
"What a coincidence that my first (European) game as Sporting manager should be against Genk.
"This is also my first home game in charge and while I wouldn't call it fate, to face Genk is unexpected.
"It is a big match, but emotionally it's normal for me."
Sporting's hopes of qualifying for the knockout stages will be dashed if they lose or draw and second-placed Videoton win. They are currently anchored to the foot of Group G with just one point, five less than Videoton.
"We are playing for our last chance to push on in the Europa League," Vercauteren said
"We have to win, obviously. I have no friends when I'm on the football field, all that interests me is securing the three points. "
Genk, who top the group with seven points, will progress to the round of 32 with two games to spare if they win and Basel fail to defeat Videoton.